Noethericity of semi-elliptical operator with constant coefficients in the range

The current thesis describes the noethericity of the linear differential semielliptical operator with constant coefficients in the range. It’s proved, that in order the operator to be noetherian it is necessary and sufficient for it to be semielliptical. In particular it is proved that the index of the semi-elliptical operator with constant coefficients in the range is equal to zero.